1. Field of the Invention
The present invention relates to a high resolution microscoping system using a convolution integration process and, more particularly, to a microscoping apparatus and method which can enlarge an image at a higher magnification than a conventional microscope, by using an electromagnetic wave, such as a light beam, an electron beam, or an X-ray beam, or a wave, such as a sound wave or an ultrasonic wave, as a probe.
2. Description of the Related Art
When a microscopic object is to be enlarged by a microscope so as to be visually observed or displayed as an image, the magnification has its limit. In optical microscopes, this limit corresponds to the diffraction limit based on the fact that light is a wave.
In optical system shown in FIG. 1, it is conventionally known that a resolvable distance .gamma..sub.0 at which two separate points on an object can be seen separately is given by ##EQU1## where .lambda. is the wavelength of light, n.sub.0 is the refractive index of a medium between the object and the lens, .theta..sub.0 is the angular aperture of the objective lens, and n.sub.0 sin.theta..sub.0 is the numerical aperture of the objective lens.
If, EQU n.sub.0 =1.5 EQU .theta..sub.0 =60.degree. EQU .lambda.=0.5 .mu.m
then, the numerical aperture is about 1.3, and the resolution is given as follows according to equation (1): EQU .gamma..sub.0 =0.24 .mu.m
However, it is very difficult to manufacture a lens having no aberrations with a numerical aperture of 1.3. Besides, it is almost impossible to increase the numerical aperture.
If the wavelength of illumination light is shortened, the resolution is increased in proportion to the wavelength. Assume that the wavelength is shortened to fall within the ultraviolet range (400 nm or less). In this case, naturally, the light cannot be seen by the unaided eyes, and the sensitivity of a currently available imaging element is not good enough for such light. In addition, optical materials for a good lens are undesirably limited. Therefore, a great reduction in wavelength is difficult to achieve.
A scanning laser microscope (laser microscope, disclosed in U.S. Pat. No. 4,733,063 "Scanning Laser Microscope with Aperture Alignment") is expected to increase the resolution. In such a microscope, similar to normal optical microscopes, an increase in resolution is limited to 30 to 40% due to the diffraction limit.
Electron microscopes which greatly exceed the resolution of such a normal optical microscope have been developed. In comparison with optical microscopes having a maximum magnification X3000, it is expected that a scanning electron microscope (SEM) can realize a magnification as high as several hundred thousands. According to such a microscope, in order to realize a high magnification, electrons are accelerated by a high voltage, and a short wave length electron beam having high energy is used. For this reason, an object tends to be damaged. Under the circumstances, a metal film is formed on a nonconductive object in order to prevent charge accumulation, or a mold of an object is formed, thus allowing measurement of the object. An electronic microscoping system has been rapidly spread because of its resolution much higher than that of an optical microscope, in spite of the fact that a microscoping operation must be performed in a vacuum in addition to the above-mentioned limitations.
The problem of image recovery is associated with the present invention from a point of view different from an increase in resolution of a microscope. In this case, the problem of image recovery includes a wide variety of problems, e.g., processing a blurred photograph to recover a sharp photograph therefrom, reconstructing an image by a CT scan and removing noise, and demodulating a band-compressed electrical signal. It is inevitable that observed data includes fluctuations and noise and hence requires extra filtering operations. The following recent book reports studies on the problems of recovery and estimation of original images and signals from such data from various aspects:
(1) H. Stark, e.d.: "Image Recovery: Theory and Application", Academic Press (1987). PA0 (2) D. Slepian and H.O. Pollak: Bell Syst. Tech. J., 40, PP. 43-64 (January 1961). PA0 (3) D.C. Youla: IEEE Trans. Circuits & Syst., CAS-25, 9, PP. 694-702 (September 1978)
In addition, since recovery of an original signal from observed data having a band-limited frequency component is equivalent to recovery of a high-frequency component which cannot be observed, in addition to the original signal, such a technique is called an ultra-high resolution technique. Various studies have been made for such a technique, e.g.,
Images recovered by these techniques, however, are just an image which should be obtained when photography is performed to prevent fluctuations and noise, a signal which should be obtained when it is received to require no extra filtering operations, and an original signal which should be obtained when it is observed so as not to be band-limited. In photography, the best image which can be photographed by a given camera can be recovered. However, these techniques are not designed to obtain a photograph having higher resolution.
As described above, in an optical microscope using a lens having no aberrations, an optical image is blurred because light is a wave and is not free from diffraction. Conventionally, it is considered that this diffraction limit is a natural phenomenon and hence cannot be overcome.